Ice
The ingredient you're most likely to ignore.
Why it counts
Ice does three jobs: it chills, it looks good, and it adds the water that softens a spirit's harder edges. Few things are as appealing as a frosted glass full of clear cubes.
It follows that bad ice can sink a cocktail exactly the way a bad spirit can. That's why serious bars spend real money on clear-ice machines, and why you'll find videos of Japanese bartenders wire-cutting a block and chipping it down to a sphere that fits a glass perfectly.
Better ice at home
Start with the best water you can get. Filtering your tap is the minimum, and spring or distilled water is worth considering. If clarity really matters to you, use distilled water, boil it twice, and let it cool completely before filling the trays. Distilling strips most of the air and minerals that cause cloudiness, and boiling drives off what's left.
For shape, standard plastic trays are fine in a pinch, but silicone trays that make large cubes and spheres are a small investment with a real payoff: less surface area means slower melting and no watery drink at the end.
The smell problem
Trays absorb freezer odors. Metal resists this better than plastic or silicone, and silicone, for all the beautiful ice it makes, picks up smells worst of all. Nobody wants ice that tastes like last week's leftovers.
So: wash your trays before a party, soap and water for standard ones, soap and water and baking soda for silicone. Better still, keep a set used only for drink ice, stored in resealable bags in a cabinet rather than living in the freezer, and away from the oven, since cooking odors travel too. Scrubbing the freezer before a big night doesn't hurt either.
Make fresh ice for each occasion. The less time it spends in the freezer, the less it tastes like the freezer.
Crushed ice
Skip the refrigerator dispenser. Get a Lewis bag and a mallet. Canvas sacks like these were standard bar equipment in the nineteenth century. Drop in fresh cubes, hit it a few times, and you have proper crushed ice. It's also an excellent way to work off a bad day.